Math Is Fun Forum

nycguitarguy

Member

Registered: 2024-02-24

Posts: 545

Properties of Absolute Value Function

Let f(x) = | x | be the absolute value function.

1. Why is the range of this function {y | y >= 0}?

2. Why does this function have an absolute minimum of 0 at x = 0?

Can the answer be that (-infinity, 0) and (0, infinity) meet at the origin where x = 0?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,196

Re: Properties of Absolute Value Function

Have you tried looking at the graph?

For positive x the graph is the same as y = x.

For negative x the graph is the same as y = -x

So, putting these together, you get a V shaped graph with the origin at the bottom of the V.

Your last line suggests you're looking at a different graph. ( y = 1/x maybe)

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

Registered: 2024-02-24

Posts: 545

Re: Properties of Absolute Value Function

Have you tried looking at the graph?

For positive x the graph is the same as y = x.

For negative x the graph is the same as y = -x

So, putting these together, you get a V shaped graph with the origin at the bottom of the V.

Your last line suggests you're looking at a different graph. ( y = 1/x maybe)

Bob

I was looking at the V-shape graph before posting this question (unless my eyes wondered away from the absolute value function to the reciprocal function). In any case, I need extra practice finding the domain range of graphs.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,196

Re: Properties of Absolute Value Function

Extra practice.

(1) y = x^2

(2) y = x^3 - 2x

(3) y = x^2/(x+4)

(4) y = sqrt(100-x^2)

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

Registered: 2024-02-24

Posts: 545

Re: Properties of Absolute Value Function

Extra practice.

(1) y = x^2

(2) y = x^3 - 2x

(3) y = x^2/(x+4)

(4) y = sqrt(100-x^2)

Bob

Ok. I will work on these and show my effort here.

nycguitarguy

Member

Registered: 2024-02-24

Posts: 545

Re: Properties of Absolute Value Function

Extra practice.

(1) y = x^2

(2) y = x^3 - 2x

(3) y = x^2/(x+4)

(4) y = sqrt(100-x^2)

Bob

For y = x^2

Vertex = (0, 0) = absolute minimum
Range = all non-negative real numbers

Domain = all real numbers

No absolute maximum.

For y = x^3 - 2x

Range = Domain = all real numbers.

No absolute minimum.

No absolute maximum.

For y = (x^2)/(x + 4)

Domain = all real numbers except x cannot be -4.

This function is not one to one. So, it does not have an inverse.

I say no range.

I an not sure about absolute minimum and absolute maximum values.

For y = sqrt{100 - x^2}

Domain: -10 <= x <= 10

Range: 0 <= y <= 10

Absolute maximum at the point (0, 10).

No absolute minimum.

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,196

Re: Properties of Absolute Value Function

Excellent attempt.  3/4 perfect.  Number 3 is very tricky. Without a graph I'd have difficulty.  It's the range that you need to work on. I recommend using the grapher.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

Registered: 2024-02-24

Posts: 545

Re: Properties of Absolute Value Function

Excellent attempt.  3/4 perfect.  Number 3 is very tricky. Without a graph I'd have difficulty.  It's the range that you need to work on. I recommend using the grapher.

Bob

I will try 3 again.